Constructed Response
Gravity
Gravity
Teacher Guide
Students will need about 30 minutes to complete these constructed response tasks.
Objectives assessed:
 Understand that the magnitude of gravitational force between two objects is
proportional to their masses and inversely proportional to the square of the distance
between them.
 Use Newton's law of gravitation to relate the distance between two objects, their
masses, and the force of attraction between them.
 Explain how the law of universal gravitation applies to objects near Earth's surface.
1. Describe how the law of universal gravitation can be seen at work during a baseball
game.
 Explain how the amount of mass of the people and equipment present is related to
the force of gravity acting on them.
 Include an explanation of how gravity affects objects close to Earth’s surface.
Correct response(s):
Sample Correct Response: Newton’s law of universal gravitation says that there is an
attractive force between any two objects in the universe. That means there is an attractive
force between Earth and all the objects on or near its surface. The gravitational force pulls
objects toward the core of the planet. Because the mass of Earth is very large, the
gravitational force between Earth and objects on Earth’s surface is also very large. If these
objects were placed in another galaxy, Earth’s pull on them would be much weaker because
they would be so far away.
There is also gravitational force acting between any two objects on Earth’s surface. The
mass of these objects is relatively small, however, so the gravitational force between them is
also small. It does not affect the objects like Earth’s gravity does.
In a baseball game, there are the players, who are held to the ground by gravitational force,
and the spectators, who are held in their seats by gravitational force. The players and
spectators have more mass than the baseballs and bats, so the force of gravity between the
people and Earth is greater than the force of gravity between a baseball and Earth.
When a baseball is pitched or thrown, gravity pulls it down toward the ground and the center
of Earth. When a player runs or jumps, he must use force to overcome the gravity that is
pulling him down. When a player slides into home plate, gravity is what pulls him to the
ground. The amount of force needed to lift a person is greater than the amount needed to
throw a ball, but in both cases, the greater force of gravity must be overcome.
Discovery Education Science
© Discovery Communications, LLC
Gravity
Response scoring tool:
Score
Content
5
Relates the law of universal gravitation to the objects on Earth’s surface,
including the force of gravity acting between the objects as well as
between Earth and the objects; explains how mass and distance are
related to the force of gravity; gives at least two specific examples of the
force of gravity in action at a baseball game.
4
Relates the law of universal gravitation to the objects on Earth’s surface,
including the force of gravity acting between Earth and the objects;
explains how mass and distance are related to the force of gravity; gives
at least two specific examples of the force of gravity in action at a
baseball game.
3
Relates the law of universal gravitation to the objects on Earth’s surface,
including the force of gravity acting between Earth and the objects;
explains how mass is related to the force of gravity; gives at least one
specific example of the force of gravity in action at a baseball game.
2
Summarizes the law of universal gravitation; gives at least one specific
example of the force of gravity in action at a baseball game.
1
Explains that Earth’s gravitational force attracts objects on or near
Earth’s surface to the planet’s center.
0
No response, or response not appropriate to the question.
Objectives assessed:
 Explain the difference between center of mass and center of gravity.
2. The spacecraft Mariner 5, shown below, was launched in 1967 to collect data about the
planet Venus.
Eventually, the spacecraft arrived in orbit near Venus. The force of gravity on Mariner 5 due
to Venus was approximately uniform during a short part of its orbit. Compare the center of
mass and the center of gravity of the spacecraft, including an explanation of your points and
definitions of each of these terms in your response.
Discovery Education Science
© Discovery Communications, LLC
Gravity
Correct response(s):
Sample Correct Response: The center of mass of an object or system is the average
location of all the mass in the system; this point can be considered the specific location of
the object. The center of gravity is the average location of the weight of the system. If the
force of gravity acting on it is uniform, as is true with this spacecraft, the center of mass and
the center of gravity are the same point.
Response scoring tool:
Score
Content
3
Defines center of mass and center of gravity, and notes that they are the
same for this object because it is symmetrical in shape and the
gravitational force acting on it is uniform.
2
Defines center of mass and center of gravity, and notes that they are the
same for this object.
1
Defines either center of mass or center of gravity.
0
No response, or response not appropriate to the question.
Objectives assessed:
 Identify each term in the equation for Newton's law of universal gravitation and explain
what it means.
 Solve problems that involve universal gravitation.
3. A 55-kg surfer at the equator falls off her board as a wave crests. What is the magnitude
of the force of gravity on the surfer? Calculate your answer using Newton’s law of
universal gravitation. (Assume the mass of Earth is 5.97 × 1024 kg and its radius at the
equator is 6.38 × 103 km.)
Correct response(s):
Sample Correct Response: We can use the equation for Newton’s law of universal
gravitation to calculate this answer. The mass of the girl (m1) is 55 kg. The mass of Earth
(m2) is 5.97 × 1024 kg. The radius of Earth at the equator is 6.38 × 103 km or 6.38 × 106 m,
which is also the distance between Earth’s center and the surfer on Earth’s surface.
Newton’s constant G is 6.67 × 10-11 N·m2/kg2. We can plug them into the equation and solve
for Fg.
Discovery Education Science
© Discovery Communications, LLC
Gravity
Gm1m2
r
2


11
24
 6.67  10 N m 2  55 kg 5.97  10 kg
kg


Fg 


6.38 10 m
2.19 10 N m 

 4.07 10 m 
6
16
13

2
2
2
Fg  540 N
Response scoring tool:
Score
Content
3
Solution includes Newton’s law of universal gravitation, correct values for
the variables, and correct solution.
2
Solution includes Newton’s law of universal gravitation and correct
values for variables.
1
Solution includes Newton’s law of universal gravitation.
0
No response, or response not appropriate to the question.
Objectives assessed:
 Solve problems involving the orbital motion of satellites using the equations for
Newton's second law of motion and the law of universal gravitation.
4. Jupiter’s moon Io orbits Jupiter at a distance of 4.22 × 105 km. The mass of Jupiter is
1.90 × 1027 kg and its radius is 71,500 km. What is Io’s acceleration due to the gravity of
Jupiter?
Correct response(s):
Sample Correct Response: To find this answer, we use both Newton’s law of universal
gravitation and the second law of motion:
Fg 
Gm1m2
r2
and F = ma. We rearrange the second
law and substitute in the law of universal gravitation for F:
a
a
F
m
Gm2
r2
The distance r between Io and Jupiter is the altitude of Io plus Jupiter's radius:
r  ralt  rJupiter
 4.22  108 m 7.15  107 m
r  4.94  108 m
Discovery Education Science
© Discovery Communications, LLC
Gravity
We can now use this value in the equation for a:
a
Gm2
r2
2

11
 6.67  10 N·m
kg 2
a 

27
 1.90  10 kg


 4.94  10 m 
8

2
3
1.27  1017 m
s2
2.44  10 m
a  5.20  101 m 2
s
a
17
2
Response scoring tool:
Score
Content
3
Solution includes Newton’s second law and the law of universal
gravitation, correct values for the variables, and correct solution.
2
Solution includes Newton’s second law and the law of universal
gravitation and correct values for variables.
1
Solution includes Newton’s law of universal gravitation.
0
No response, or response not appropriate to the question.
Discovery Education Science
© Discovery Communications, LLC